Answer:
see explanation
Step-by-step explanation:
(a)
Given
2k - 6k² + 4k³ ← factor out 2k from each term
= 2k(1 - 3k + 2k²)
To factor the quadratic
Consider the factors of the product of the constant term ( 1) and the coefficient of the k² term (+ 2) which sum to give the coefficient of the k- term (- 3)
The factors are - 1 and - 2
Use these factors to split the k- term
1 - k - 2k + 2k² ( factor the first/second and third/fourth terms )
1(1 - k) - 2k(1 - k) ← factor out (1 - k) from each term
= (1 - k)(1 - 2k)
1 - 3k + 2k² = (1 - k)(1 - 2k) and
2k - 6k² + 4k³ = 2k(1 - k)(1 - 2k)
(b)
Given
2ax - 4ay + 3bx - 6by ( factor the first/second and third/fourth terms )
= 2a(x - 2y) + 3b(x - 2y) ← factor out (x - 2y) from each term
= (x - 2y)(2a + 3b)
Answer:
the answer is c. see picture
The veretx is normally the minimum value
hack:
for f(x)=ax²+bx+c
the x value of the vertex is -b/2a
so
f(x)=1x²-16x+71
x value is -(-16)/(2*1)=16/2=8
find f(8) to find y value of vertex
f(8)=8²-16(8)+71
f(8)=64-128+71
f(8)=7
the vertex is (8,7)
the minimum value is 7
Answer:



Step-by-step explanation:
Given
Let the three sides be represented with A, B, C
Let the angles be represented with 
[See Attachment for Triangle]



What the question is to calculate the third length (Side B) and the other 2 angles (
)
Solving for Side B;
When two angles of a triangle are known, the third side is calculated as thus;

Substitute:
,
; 




Take Square root of both sides



<em>(Approximated)</em>
Calculating Angle 

Substitute:
,
; 




Subtract 180 from both sides


Divide both sides by -144



Take arccos of both sides



<em>(Approximated)</em>
Calculating 
Sum of angles in a triangle = 180
Hence;



Make
the subject of formula


H would decrease either way because h is a variable for a certain number. that number would usually be divided from both sides. you would be eliminating x from the equation. 125x/h. by dividing you are creating a smaller number. by dividing you are decreasing. you're welcome. :)